University of Groningen
Vancomycin Pharmacokinetics Throughout Life
Colin, Pieter J; Allegaert, Karel; Thomson, Alison H; Touw, Daan J; Dolton, Michael; de Hoog,
Matthijs; Roberts, Jason A; Adane, Eyob D; Yamamoto, Masato; Santos-Buelga, Dolores
Published in:Clinical Pharmacokinetics DOI:
10.1007/s40262-018-0727-5
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Colin, P. J., Allegaert, K., Thomson, A. H., Touw, D. J., Dolton, M., de Hoog, M., Roberts, J. A., Adane, E. D., Yamamoto, M., Santos-Buelga, D., Martín-Suarez, A., Simon, N., Taccone, F. S., Lo, Y-L., Barcia, E., Struys, M. M. R. F., & Eleveld, D. J. (2019). Vancomycin Pharmacokinetics Throughout Life: Results from a Pooled Population Analysis and Evaluation of Current Dosing Recommendations. Clinical
Pharmacokinetics, 58(6), 767-780. https://doi.org/10.1007/s40262-018-0727-5
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Vol.:(0123456789) https://doi.org/10.1007/s40262-018-0727-5
ORIGINAL RESEARCH ARTICLE
Vancomycin Pharmacokinetics Throughout Life: Results
from a Pooled Population Analysis and Evaluation of Current Dosing
Recommendations
Pieter J. Colin1,2 · Karel Allegaert3,4,5 · Alison H. Thomson6 · Daan J. Touw7,8 · Michael Dolton9 · Matthijs de Hoog10 ·
Jason A. Roberts11 · Eyob D. Adane12 · Masato Yamamoto13 · Dolores Santos‑Buelga14 · Ana Martín‑Suarez14 ·
Nicolas Simon15 · Fabio S. Taccone16 · Yoke‑Lin Lo17,18 · Emilia Barcia19 · Michel M. R. F. Struys1,20 · Douglas J. Eleveld1
© The Author(s) 2019
Abstract
Background and Objectives Uncertainty exists regarding the optimal dosing regimen for vancomycin in different patient populations, leading to a plethora of subgroup-specific pharmacokinetic models and derived dosing regimens. We aimed to investigate whether a single model for vancomycin could be developed based on a broad dataset covering the extremes of patient characteristics. Furthermore, as a benchmark for current dosing recommendations, we evaluated and optimised the expected vancomycin exposure throughout life and for specific patient subgroups.
Methods A pooled population-pharmacokinetic model was built in NONMEM based on data from 14 different studies in different patient populations. Steady-state exposure was simulated and compared across patient subgroups for two US Food and Drug Administration/European Medicines Agency-approved drug labels and optimised doses were derived.
Results The final model uses postmenstrual age, weight and serum creatinine as covariates. A 35-year-old, 70-kg patient
with a serum creatinine level of 0.83 mg dL−1 (73.4 µmol L−1) has a V
1, V2, CL and Q2 of 42.9 L, 41.7 L, 4.10 L h−1 and
3.22 L h−1. Clearance matures with age, reaching 50% of the maximal value (5.31 L h−1 70 kg−1) at 46.4 weeks
postmen-strual age then declines with age to 50% at 61.6 years. Current dosing guidelines failed to achieve satisfactory steady-state exposure across patient subgroups. After optimisation, increased doses for the Food and Drug Administration label achieve consistent target attainment with minimal (± 20%) risk of under- and over-dosing across patient subgroups.
Conclusions A population model was developed that is useful for further development of age and kidney function-stratified dosing regimens of vancomycin and for individualisation of treatment through therapeutic drug monitoring and Bayesian forecasting.
Electronic supplementary material The online version of this article (https ://doi.org/10.1007/s4026 2-018-0727-5) contains supplementary material, which is available to authorized users. * Pieter J. Colin
p.j.colin@umcg.nl
Extended author information available on the last page of the article
Key Points
Current dosing recommendations fail to achieve consist-ent vancomycin exposure throughout life and across patient subgroups.
This pharmacokinetic model for vancomycin adequately characterises vancomycin pharmacokinetics across a broad range of patient populations, including those at the extremes of age and weight.
1 Introduction
The glycopeptide antibiotic vancomycin plays an impor-tant role in the treatment of Gram-positive bacterial infec-tions. It is currently considered a key therapeutic option in the context of the treatment of serious infections (e.g. community- and hospital-acquired pneumonia, compli-cated skin and soft-tissue infections, infective endocardi-tis) and for the empiric treatment of patients at high risk of infections caused by methicillin-resistant Staphylococcus aureus or multidrug-resistant Staphylococcus epidermidis
[1, 2].
Although vancomycin has been in clinical use since its first registration almost six decades ago, questions with respect to the optimal dosing regimen remain. Con-sequently, a plethora of reports on subpopulation- and context-specific pharmacokinetics and derived dosing regimens have surfaced over the last 25 years. In 2012,
these numerous population-pharmacokinetic (PK) studies
led Marsot and co-workers [3] to conclude that initial
dos-ing regimens for vancomycin should depend on creatinine clearance and body weight in adults, and creatinine clear-ance, body weight and age in children. The assessment report on vancomycin drug products issued in 2017 by the
European Medicines Agency [1] is in line with the
rec-ommendations by Marsot and co-workers. Nevertheless, it also highlights some known unknowns. For example, the report comments that specific dosing regimens might be required for neonatal and elderly populations and for patients with renal impairment.
Besides getting the initial dose right, optimisation of vancomycin exposure entails the use of therapeutic drug monitoring (TDM), especially in populations where PK variability is large (e.g. preterm neonates, critically ill
patients) [1]. Individualised dosing based on TDM data is
most efficiently achieved through Bayesian forecasting of PK parameters based on an a priori population-PK model. This technology is currently offered by a range of TDM
software packages [4], such as DoseMe® (DoseMe Pty
Ltd., Brisbane, QLD, Australia), InsightRx® (Insight Rx
Inc., San Francisco, CA, USA), MwPharm ++® (Mediware
a.s., Prague, Czech Republic) and DosOpt (University of
Tartu, Tartu, Estonia) [5].
At present, different vancomycin population-PK models are, however, used across these software packages; and within a package often different models are used for differ-ent patidiffer-ent subpopulations. This poses a challenge to clini-cians who have to consider the limitations of the models they utilise. Moreover, the clinician might have to switch models when treating different patient populations.
It has previously been shown that when applied to external datasets, there are wide differences in the
per-formance of various currently used PK models [6, 7]. In
anaesthesia, this has led to data-sharing initiatives with the intent of replacing different subgroup-specific models
with a single pooled population-PK model [8, 9]. Such
a model is expected to be more generalisable than other models, making it simpler and more useful for everyday
clinical use [10].
In this study, we aimed to develop a single PK model for vancomycin, derived from a broad dataset covering the extremes of patient characteristics. Moreover, as a bench-mark for current dosing recommendations, we performed simulations using the final population-PK model and eval-uated the expected vancomycin exposure throughout life and for specific patient subgroups. Finally, based on these simulations optimised doses were recommended.
2 Materials and Methods
2.1 Component Datasets
Studies on vancomycin pharmacokinetics were identi-fied though a PubMed search (until 27 September, 2017) using search terms: “vancomycin AND population AND pharmacokinetics [Title/Abstract]” OR “vancomycin AND pharmacokinetics [Title/Abstract]”. We excluded studies of patients receiving continuous renal replacement ther-apy, haemodialysis, haemodiafiltration, extra-corporeal membrane oxygenation and non-intravenous administra-tion of vancomycin. Corresponding or senior authors from these studies were invited to contribute their anonymised data and participate in this modelling study. All studies obtained necessary institutional review board approval, as declared in the original papers or as declared by the corresponding or senior author (personal communication).
Postmenstrual age (PMA), postnatal age (PNA), weight, height and serum creatinine (SCR) were extracted from the datasets. Postmenstrual age for patients other than neonates was assumed to be 40 weeks longer than the recorded postnatal age (years). Missing values for SCR were imputed as the population median SCR from that study. Missing values for height were imputed as the popu-lation median height from that study or from a similar study (for neonatal studies with missing height) or with height data from a national health survey in that specific population.
Questionable covariate data were corrected whenever possible. These primarily concern overlapping drug infu-sion records and unrealistic combinations of age, weight and height within a subject. To avoid computational difficulties during model building due to excessively long follow-up times, the dataset was restricted to observations from the first 31 days of therapy.
2.2 Population‑Pharmacokinetic Modelling
The vancomycin concentration vs. time data were fitted
using the FOCE-I estimation algorithm in NONMEM®
(Version 7.3; GloboMax LLC, Hanover, MD, USA). The “tidyverse” package (Version 1.1.1.; Wickham H. 2017)
in R® (R Foundation for Statistical Computing, Vienna,
Austria) was used to graphically assess the goodness of fit and for simulations.
As a starting point, one-, two- and three-compartmental PK models were fitted to the data. Inter-individual vari-ability on the typical population parameter estimates was assumed to be log-normally distributed. Residual unex-plained variability was modelled using a combined propor-tional and additive error model. Inter-occasion variability
was not tested in the model owing to difficulties in defining an occasion in the context of this dataset where dosing and sampling times/frequency vary considerably.
Modifications to the structural and/or covariate model were accepted only if they resulted in a decrease in the objective function value (OFV) and an increased in-sample predictive performance. A decrease in OFV was judged sta-tistically significant if inclusion of an additional parameter decreased the OFV by more than 3.84 points. As a measure of in-sample prediction performance, the absolute relative
prediction errors (APEs) were calculated (Eq. 1) by
compar-ing the measured vancomycin concentrations for each
indi-vidual i at time point j (VANij) with the population-predicted
concentrations (PRED). The median of the distribution of APEs (MdAPE) was used to compare the imprecision of candidate models during model building and to compare the final model against earlier published models.
To ascertain that model building was not driven by the most populated subgroup, we stratified the calculation of the prediction error. The following subgroups were created: pre-term and pre-term newborns (PMA < 0.87 years), children and adolescents (age < 18 years), adults (age < 65 years), elderly (age < 80 years), very elderly (age ≥ 80 years), underweight
adults (age > 18 years and body mass index < 18.5 kg m−2)
and obese adults (age > 18 years and BMI > 30 kg m−2).
Dur-ing model buildDur-ing, the average MdAPE across the afore-mentioned subgroups was taken as an overall measure of predictive performance. Covariates tested for inclusion in the model were: weight (kilograms), PMA (years), PNA
(days), SCR (mg dL−1), sex, critical illness and presence of
severe burn injuries. Height and related covariates such as body mass index and fat-free mass were not tested as height was missing in most neonates and some adults.
2.3 A Priori Included Covariate Models
In line with earlier work by Holford et al. [11] and
Ger-movsek et al. [12, 13] prior to inclusion of additional
covari-ates in the model we corrected for size and maturational changes. For this, PK parameters were scaled to weight
according to allometric theory [14], with an exponent of
1 for volume terms (V1, V2, V3) and an exponent of 0.75
for clearance terms (CL, Q2, Q3). A sigmoidal maturation function was used to scale clearance with PMA according
to Eq. 2 with γ defining the steepness of the non-linear
rela-tionship and PMA50 being the PMA when clearance reaches
50% of maximal values. (1) APE(%) =||| | | VANij− PREDij PREDij | | | | | × 100%. (2)
Maturation function = PMA
𝛾
PMA𝛾+ PMA𝛾50.
2.4 Testing Serum Creatinine as a Covariate in the Model
The influence of SCR on clearance was tested using an
expo-nential function as shown in Eq. 3. This function predicts
decreasing clearance with increasing SCR values with θSCR
defining the steepness of the relationship. Serum creatinine was included in the dataset as a time-varying covariate with backward constant interpolation between observations.
Parameter values were standardised by centering SCR
observations according to a standardised SCR (SCRstd)
value. Different approaches for defining SCRstd were
compared. A first approach consisted of using the median observed SCR from the dataset. Other approaches were explored in an effort to derive age-, weight- and sex-adjusted
SCRstd values. For this, empiric functions were fitted to the
covariate data using fractional polynomial regression (R package “mfp: Multivariable Fractional Polynomials”;
Ver-sion 1.5.2) in line with the work of Ceriotti et al. [15], or
custom non-linear models in R®.
2.5 Evaluation and Optimisation of Current Dosing Recommendations
As examples of contemporary dosing guidelines for vanco-mycin approved by the European Medicines Agency and the US Food and Drug Administration (FDA), we used the sum-mary of product characteristics (SmPC) for “Vancomycin 500 mg Powder for Solution for Infusion” (Consilient Health
Ltd; available from www.medic ines.org.uk; consulted on 23
May, 2018) and the label for “Vancomycin Hydrochloride for Injection USP” (ANI Pharmaceuticals, Inc.; available
from www.fda.gov; consulted on 23 May, 2018). The
posol-ogies outlined by the SmPC and the FDA label are summa-rised in Tables S1 and S2 of the Electronic Supplementary Material (ESM), respectively.
Steady-state vancomycin exposure was simulated using the post hoc-predicted clearance for all patients in our
data-set according to Eq. 4:
where AUC 24 h is the area under the concentration–time
curve for a 24-h period in steady state and DOSE and τ are the amount of vancomycin administered and the dosing
interval, respectively. The predicted AUC 24 h was then used
to calculate the proportion of patients who were under- and
over-dosed. Under-dosing was assumed when the AUC 24h
was below 400 mg L−1 h, a frequently cited threshold for
(3) FScr= e(−𝜃SCR×(SCR−SCRstd)). (4) AUC24 h= DOSE ×24 𝜏 CL ,
efficacy [16, 17] for the treatment of pathogens with a
mini-mum inhibitory concentration of 1 mg L−1. Over-dosing was
defined as an AUC 24h exceeding 700 mg L−1 h, a recently
advocated safety threshold for renal toxicity [18].
In the final part of this study, we attempted to optimise the daily doses in the SmPC and the FDA label. For this, in line with the above, post hoc-predicted clearance for all patients was used to predict the proportion of patients achieving
an AUC 24h above 400 mg L−1 h and below 700 mg L−1
h (fTarget). A non-linear optimisation routine based on the
Nelder-Mead Simplex [19] as implemented in R® (R
pack-age “nloptr”; Version 1.0.4) was used to optimise fTarget using
the doses in the SmPC and the label as control variables. For practical purposes, optimised daily doses were rounded to
the nearest 50 mg and 0.5 mg kg−1.
3 Results
3.1 Data
In total, 39 publications were identified. All senior and/or corresponding authors for these publications were contacted via e-mail on multiple occasions. We obtained 14 previously
published data sets [20–33]. Our pooled dataset contains
information across a broad range of patient subgroups
rang-ing from premature neonates [20, 24, 30, 32] to extremely
obese patients [26] and from adult Japanese healthy
volun-teers [27] to critically ill and trauma patients [25, 31, 33].
A summary of the included studies is shown in Table 1.
The distributions of patient characteristics and vancomycin concentrations are shown in Fig. S1 of the ESM. In total, 8300 vancomycin drug concentrations from 2554 individuals were included in the dataset. Individuals were adults (720), newborns (559), elderly patients (512), obese adults (274), very elderly patients (213), underweight adults, (158) and children and adolescents (118).
Initial analysis of the dataset identified outliers (n = 10). The data for these individuals were primarily biased because of missing dosing information prior to the first observation, potential sampling errors (e.g. reported vancomycin
con-centrations > 100 mg L−1) or dosing regimens that were
sig-nificantly different from other comparable individuals from the same study. Because of the small number of outliers identified (0.4% of individuals), we decided to remove these patient records from the dataset.
3.2 Population‑Pharmacokinetic Modelling
We found that a two-compartment model better described the data compared with a one-compartment model (ΔOFV = − 1155). A three-compartment model had a lower
OFV (ΔOFV = − 85). However, goodness-of-fit plots for both models were indistinguishable and likelihood
profil-ing [34] revealed high uncertainty on the estimate for the
inter-compartmental clearance to the slow peripheral com-partment (Q3). Therefore, we decided to retain the two-compartment model as the final model.
We found significant maturation in vancomycin clearance, with 50% of maximal clearance being reached by 46.4 weeks
PMA (PMA50). After correcting for maturation, it became
apparent that vancomycin clearance deteriorates with age-ing. The sigmoidal function fitted to describe the declining clearance with age revealed that 50% of maximal clearance
is lost by 61.6 years PMA (AGE50). Figure 1 shows the
typical-for-PMA standardised clearance (L h−1 70 kg−1) for
all patients in our dataset. Figure 1 also shows the
matura-tion–decline function as estimated by Lonsdale et al. [35] in
a recent pooled analysis of three commonly used beta-lactam antibiotics.
After accounting for size- and age-related changes in van-comycin pharmacokinetics, we tested the influence of SCR
on clearance according to Eq. 3. Table 2 provides an
over-view of the different model building steps and shows the
dif-ferent approaches taken to define SCRstd. When the median
observed SCR (0.80 mg dL−1 or 70.7 µmol L−1) is used
as SCRstd, the lowest OFV is obtained (ΔOFV = − 1810).
However, this approach led to an increase in the estimates for
PMA50 and AGE50. A fractional polynomial model relating
SCRstd to PNA, gestational age, weight and sex performed
less well (ΔOFV = − 1692). However, standardisation of SCR values using this approach had no influence on the
estimates for PMA50 and AGE50. Ultimately, we found that
the empiric function producing the lowest OFV with the
least influence on the estimates for PMA50 and AGE50 was
a non-linear function relating SCRstd to PMA (Eq. 5).
A plot of the predicted SCRstd as a function of PMA is
shown in Fig. S2 of the ESM. Figure S2 also shows the
SCRstd used in the work of Johansson et al. [36] and
Hen-nig et al. [37], which is based on the reference intervals
reported by Ceriotti et al. [15] and Junge et al. [38] When
we implemented the latter approach, we found a similar decrease in OFV compared to our best performing function (ΔOFV = − 1790 vs. −1805, respectively). However, as seen
in Table 2, under this approach the estimates for PMA50
and AGE50 slightly increase (+1.8 weeks and +4.1 years,
respectively). Furthermore, as seen in Fig. S2 of the ESM,
the predicted SCRstd does not align well with the median of
our observed SCR values. Therefore, we decided to include
the empiric function described in Eq. 5 in our final model.
The inclusion of SCR decreased in-sample MdAPEs for all subgroups ranging from − 0.7% for children and adolescents (5) SCRstd= e(−1.228+log10(PMA(yr))×0.672+6.27×e(−3.11×PMA(yr)).
Table 1 De tails of t he com ponent dat ase ts. The dis tribution of patient co var iates is summar ised b y t he median and t he r ang e; t he per cent ag e of missing v alues is sho wn in sq uar e br ac ke ts ICU intensiv e car e unit, PMA pos tmens trual ag e, PNA pos tnat al ag e, SCR ser um cr eatinine a PMA in y ears w as der iv ed fr om t he dat ase ts or assumed t o be PN A plus g es tational ag e wit h a def ault of 40 wk f or subjects wit h missing g es tational ag e b Number of doses pr ior t o t he firs t plasma sam ple c PMA in t his s tudy w as missing but w as assumed t o be eq ual t o pos tconcep tual ag e d In t his s tudy , all patients r eceiv ed a loading dose f ollo wed b y a continuous infusion e Co var iate v alues at t
he time of inclusion int
o t he s tudy ar e sho wn, dur ing t he modelling t hese co var iates w er e consider ed t o be time v ar ying and t heir entir e time course w as t ak en int o account Dat ase t N Patients Inclusion % Male PMA (y) a,e PN A (d) e W eight (k g) e Height (m) SCR (mg dL −1) e No. of sam ples No. of doses b Alleg aer t e t al. [ 11 ] 247 Pr ematur e neo -nates 2002–2006 54.7 0.60 (0.46–0.71) 11 (1–27) 1.20 (0.42–2.63) 0.37 (0.26–0.48) [16%] 0.73 (0.39–2.12) [0.1%] 2 (1–9) 2 (1–6) Thomson e t al. [ 12 ] 496 Adult patients 1991–2007 39.3 67.8 (16.8–97.8) – 70.0 (35.0–159) 1.70 (1.42–1.98) [20%] 1.10 (0.34–6.48) 3 (1–19) 2 (1–11)
van der Meer e
t al. [ 13 ] 389 Paediatr ic, adult and elder ly patients 2001–2010 55.8 65.9 (2.58–97.8) – 70.0 (8.70–160) 1.70 (0.70–2.02) 0.79 (0.15–9.75) 2 (1–16) 2 (1–16) Dolt on e t al. [ 14 ] 70
Adult patients wit
h/wit hout bur n injur ies 2000–2007 78.6 52.8 (15.8–95.8) – 68.0 (42.5–116) 1.70 (1.55–1.80) [80%] 0.64 (0.24–6.11) [4.3%] 3 (1–32) 3 (1–43) de Hoog e t al. [ 15 ] 130 Pr ematur e neo -nates 1992–1997 54.6 0.60 (0.51–0.84) c13 (3–27) 1.07 (0.51–4.41) [100%] 0.57 (0.26–2.04) [85%] 2 (2–3) 2 (1–2) Rober ts e t al. [ 16 ] 204 Adult sep tic cr iti -call y ill patients 2008–2009 62.2 59.8 (18.8–86.8) – 74.5 (35.0–140) 1.70 (1.53–1.90) 0.75 (0.20–4.4) 3 (1–3) 2 (2–2) d Adane e t al. [ 17 ] 29 Extr emel y obese patients 2012–2013 65.5 46.8 (24.8–71.8) – 148 (111–282) 1.78 (1.50–1.96) 1.00 (0.60–1.40) [3.0%] 3 (2–7) 5 (1–6) Yamamo to e t al. [ 18 ] 106
Adult Japanese patients and healt
hy contr ols 2004–2005 66.0 67.1 (20.8–100) – 50.8 (28.6–97.0) [100%] 0.70 (0.20–2.60) 2.5 (1–16) 4 (1–18) Re villa e t al. [19) 190
Adult Spanish ICU patients
1999–2004 65.8 65.8 (18.8–85.8) – 70.5 (45.0–150) 1.67 (1.45–1.85) [7.0%] 1.00 (0.60–7.21) 2 (1–19) 4 (1–68) Buelg a e t al. [ 20 ] 286
Adult Spanish patients wit
h haemat ological malignancies 1989–1999 61.1 54.3 (15.8–84.8) – 64.0 (41.0–100) 1.63 (1.44–1.85) 0.86 (0.40–3.00) 3 (1–12) 6 (1–57) Oudin e t al. [21) 67
Neonates and pae
-diatr ic patients 2006–2008 61.1 0.60 (0.52–0.88) 13 (4–95) 1.06 (0.68–4.45) [100%] 0.60 (0.20–3.12) 2 (1–6) 3 (1–6) Cr ist allini e t al. [ 22 ] 107 Adult cr iticall y ill patients 2012–2013 72.0 59.8 (18.8–89.8) – 75.0 (40.0–142) 1.75 (1.50–1.92) 0.90 (0.20–4.70) 3 (2–3) 2 (2–2) d Lo e t al. [ 23 ] 116 Pr ematur e Mala y-sian neonates 1999–2005 56.9 0.55 (0.45–0.65) 5 (1–39) 0.90 (0.50–2.00) [100%] 0.88 (0.33–1.62) 6 (2–27) 2 (1–20) Medellín-Gar iba y et al. [ 24 ] 117 Spanish tr auma patients 2010–2013 44.4 77.8 (37.8–101) – 71.0 (38.0–110) 1.60 (1.40–1.82) 0.74 (0.25–2.00) 2 (1–16) 5 (1–51)
to − 10.2% in elderly patients. Inclusion of SCR as a base-line covariate rather than a time-varying covariate was sig-nificantly worse (ΔOFV = + 876).
At this step in model development, we tested
compart-mental allometry for clearance and Q2, scaling them
allomet-rically to the estimated size of the corresponding
compart-ment (V1 and V2). In line with earlier work on propofol [8],
remifentanil [9] and dexmedetomidine [39],
compartmen-tal allometry improved the goodness of fit (ΔOFV = − 212) without disturbing the interpretation of the fixed-effect parameters in the models.
Altered pharmacokinetics was observed in two composite datasets. On the one hand, in the study by Buelga and
co-workers on patients with haematological malignancies [29],
clearance was significantly higher (+29.4%). On the other
hand, the study by Lo and co-workers [32], who used
heel-prick sampling as opposed to arterial/venous sampling, we
found a lower V1 (− 31.2%) and Q2 (− 59.7%). Accounting
for these subgroup-specific effects resulted in a better fit (ΔOFV = − 184 and − 115, respectively).
To achieve adequate numeric stability of the model, i.e. smooth gradient minimisation and acceptable likelihood
profiles, we removed the estimate for the population vari-ability on Q2 (ΔOFV = + 5.0).
The final population-PK model is shown in Eqs. 6–13 and
Table 3, the NONMEM output for the final model is shown
in the ESM. (6) CL(L h−1) = 𝜃CL× ( V1 𝜃V1 )0.75 × FMat× FDecline × FSCR× ( 1+ 𝜃STDY10 ) × e𝜂1 (7) V1(L) = 𝜃V1× ( FSize)1×(1 − 𝜃STDY13_V1)× e𝜂2 (8) V2(L) = 𝜃V2×(FSize)1× e𝜂3 (9) Q2(L h−1) = 𝜃Q2× ( V2 𝜃V2 )0.75 ×(1 − 𝜃STDY13_Q2) (10) FSize= WGT(kg) 70 Fig. 1 Standardised clearance
[CLstd] (L h−1 70 kg−1) for vancomycin throughout life. Typical vancomycin clearance according to our final model is shown with a solid black line. Post-hoc CLstd values for all patients in our dataset are shown with solid grey circles. The grey shaded area denotes the region between the 10 and 90% percentile of all observa-tions. The dashed black line is the maturation–decline function for beta-lactam antibiotics according to Lonsdale et al. [35] PMA postmenstrual age
0 5 10 0.4 0.6 0.8 1.0 2.0 4.0 6.0 8.0 10.0 20.0 40.0 60.0 80.0 PMA (years) CLst d ( Lh −1 70 kg −1 )
Table
2
Model building hier
ar ch y CL v ancom ycin clear ance, Fr acP ol y fr actional pol ynomial r eg ression, GA g es tational ag e, IIV inter -individual v ar iability , MdAPE in-sam
ple median absolute r
elativ e pr ediction er ror , OFV objectiv e function v alue, PMA pos tmens trual ag e, PNA pos tnat al ag e, Q2 inter -com par tment al clear ance, Ref. ref er ence, SCR ser um cr eatinine, SCR std st andar dised SCR, V1 centr al v olume of dis tribution, V2 per ipher al v olume of dis tribution, WGT w eight No . Ref. Descr ip tion OFV ΔOFV PMA 50 (wk) γ1 AG E50 (y) γ2 IIV CL (%) IIV V1 (%) IIV Q2 (%) IIV V2 (%) MdAPE (%) 1 Allome try + matur ation 36,846 – 32.8 4.44 – – 58.0 34.6 66.3 151 39.0 2 1 PMA as a co var iate on CL ( FDecline ; Eq. 12 ) 36,150 − 696 44.2 3.29 66.0 2.66 47.7 33.9 65.3 146 32.6 3 2 SCR on CL (Eq. 13 ) wit h SCR std = 0.80 mg dL −1 (70.7 µmol L −1) 34,340 − 1810 52.5 2.28 79.8 3.32 34.6 34.3 66.5 122 28.0 4 2 SCR on CL (Eq. 13 ) wit h SCR std as a nonlinear function of PMA 34,345 − 1805 44.7 3.32 67.4 2.77 34.7 34.7 62.2 123 28.2 5 2 SCR on CL (Eq. 13 ) wit h SCR std accor ding t o Johansson et al. 36 34,360 − 1790 46.5 2.77 71.5 2.34 34.9 34.1 67.9 121 28.3 6 2 SCR on CL (Eq. 13 ) wit h SCR std as a fr actional pol yno -mial eq uation of PN A , G A , W GT , M1F2 34,458 − 1692 45.2 3.16 67.4 2.94 35.9 33.4 54.3 119 28.8 7 4 Com par tment al allome try 34,133 − 212 47.6 2.91 62.8 2.58 27.3 32.6 72.3 92.1 28.3 8 7 STD Y13 as a co var iate on V1, Q2 33,949 − 184 46.5 2.86 64.1 2.69 28.8 28.2 31.9 96.6 27.4 9 8 STD Y10 as a co var iate on CL 33,834 − 115 46.6 2.86 61.6 2.24 27.6 27.7 32.9 95.4 26.7 10 9 Remo val of IIV on Q2 33,839 + 5 46.4 2.89 61.6 2.24 27.9 27.3 – 97.9 26.8
In these equations, CL (L h−1) is vancomycin clearance,
V1 (L) and V2 (L) are the central and peripheral volume
of distribution and Q2 (L h−1) is the inter-compartmental
clearance. FSize, FMat, FDecline and FSCR describe size-related
changes, maturational changes, age-induced deterioration and SCR-related changes in vancomycin pharmacokinetics,
respectively. θSTDY10, θSTDY13_V1 and θSTDY13_Q2 denote the
increased clearance in patients with haematological
malig-nancies and the effect of heel-prick sampling on V1 and Q2.
Symbols η1–η3 denote inter-individual variability (with
vari-ances ω1–ω3) of the typical PK parameters.
Backwards elimination of FSize, FMat, FDecline or FSCR from
the model consistently resulted in an increased OFV and increased unknown inter-individual variability in clearance (data not shown). Goodness-of-fit plots for the final model
are shown in Fig. 2. Figures S3, S4 and S5 of the ESM
show the goodness-of-fit plots stratified by study and the
prediction-variance-corrected visual predictive check [40]
for the pooled data and data stratified by patient category, (11) FMat= PMA(wk) 𝛾1 PMA(wk)𝛾1+ PMA𝛾1 50 (12) FDecline= PMA(yr) −𝛾2
PMA (yr)−𝛾2+ AGE𝛾2
50
(13) FSCR= e(−𝜃SCR×(SCR(mgdL−1)−SCRstd)),
respectively. Overall, these diagnostics show that our final model is adequately developed.
3.3 Evaluation and Optimisation of Current Dosing Recommendations
The distribution of predicted steady-state vancomycin
AUC 24h resulting from the dosing recommendations in the
SmPC and the FDA label are shown in Fig. 3. The
propor-tion of patients achieving an AUC 24h below 400 mg L−1 h
(fAUC<400), between 400 and 700 mg L−1 h (fTarget), and above
700 mg L−1 h (f
AUC>700) are shown in Tables S3 and S4 of
the ESM.
Based on the dosing regimen in the SmPC, 19% of
patients attain an AUC 24h below 400 mg L−1 h, whilst 46%
of patients attain an AUC 24h above 700 mg L−1 h. Elderly
(76%), very elderly (70%) and obese patients (81%) are
mainly at risk for attaining a steady-state AUC 24h above
700 mg L−1 h, whereas for underweight adults (25%),
new-borns (43%), and children and adolescents (65%) a
consider-able proportion of patients is expected to attain an AUC 24h
below 400 mg L−1 h.
The dosing regimens in the FDA-approved label result in a more consistent steady-state exposure with a very low risk
of attaining an AUC 24h above 700 mg L−1 h across patient
subgroups. However, except for newborns, all patient
sub-groups are significantly at risk for a steady-state AUC 24h
below 400 mg L−1 h, with probabilities ranging from 52%
in very elderly patients to 70% in children and adolescents. The optimised daily doses for the SmPC and FDA label
are shown in Table 4. In general, optimised daily doses are
Table 3 Parameter estimates and associated relative standard errors (RSEs) for the final population-pharmacokinetic model. Inter-individual variability (IIV) associated with the typical parameters is expressed as coefficient of variation %
a Calculated according to: √e𝜔− 1 × 100% b Derived from log-likelihood profiling c Expressed as standard deviation
Final model
Parameter Estimate (RSE %b) IIVa (RSE %b) η Shrinkage, %
𝜃CL (L h−1 70 kg−1) 5.31 (1.6) 27.9 (3.2) 29.8 𝜃V1 (L 70 kg−1) 42.9 (1.9) 27.3 (9.8) 42.7 𝜃V2 (L 70 kg−1) 41.7 (3.5) 97.9 (5.7) 47.0 𝜃Q2 (L h−1 70 kg−1) 3.22 (7.1) – – PMA50 (wk) 46.4 (4.2) – – γ1 2.89 (7.6) – – AGE50 (y) 61.6 (4.0) – – γ2 2.24 (6.5) – – 𝜃SCR 0.649 (2.3) – – 𝜃STDY10 0.294 (9.2) – – 𝜃STDY13_V1 0.312 (11) – – 𝜃STDY13_Q2 0.597 (10) – –
Residual error (proportional) 21.5 (3.2) – –
higher. Exceptions are adults and children with an estimated
glomerular filtration rate < 50 mL.min−1, where the
opti-mised daily doses for the SmPC are 14.5 and 28.5 mg kg−1
instead of 15 and 30 mg kg−1. For both the optimised SmPC
and the FDA label, fTarget increases consistently across
sub-groups with the overall fTarget increasing from 35 to 46% and
37 to 60% for the SmPC and the FDA label, respectively. For
the optimised label, fTarget is > 50% in all subgroups and the
risk for over- or under-dosing is consistent (± 20%) across subgroups. However, for the optimised SmPC, children and adolescents (30%) and underweight adults (46%) remain at risk for under-dosing, whereas elderly patients (46%), very elderly patients (53%) and obese patients (58%) are at risk for over-dosing.
4 Discussion
In this population-PK modelling study, we showed that van-comycin pharmacokinetics undergoes significant changes throughout human life. Besides size-related changes in clearance, maturation is the main driver for clearance
during early childhood with 90% of adult clearance being reached by 2 years PMA. Between 3 and 16 years PMA,
size-corrected clearance is highest (> 5.05 L h−1 70 kg−1).
Afterwards, clearance deteriorates significantly,
reach-ing 2.66 h−1 70 kg−1 (i.e. 50% of maximum clearance) by
61.6 years PMA. Not surprisingly, we found that SCR is a significant covariate on clearance for both between- and within-subject variability. When SCR decreases or increases
0.20 mg dL−1 (17.7 µmol L−1) from the typical-for-PMA
SCRstd, clearance changes with + 13.8 and − 12.2%,
respectively.
According to our model, typical vancomycin clearance
in a 60-year-old, 65-kg patient with a SCR of 0.97 mg dL−1
(85.7 µmol.L−1) is 2.55 L h−1 (0.039 L h−1 kg−1).
Vancomy-cin clearance in a 32-week, 1.5-kg neonate with a SCR of
0.64 mg dL−1 (56.6 µmol L−1) is 0.0756 L h−1 (0.0504 L.h−1.
kg−1). Both values are in line with the range of clearance
estimates reported by Marsot et al. 3 for adults (0.031–0.086
L h−1 kg−1) and paediatric patients (0.020–0.112 L h−1 kg−1).
In contrast to Marsot et al. [3] who reported different
esti-mates for vancomycin volume of distribution for adults
(0.864 L kg−1) and children (0.565 L kg−1), we found that
Fig. 2 Goodness-of-fit plots for the final population-pharma-cokinetic model. Scatterplots show the distribution of the observed vancomycin con-centrations (Observed Cplasma) vs. population and individual predictions and the (absolute) conditionally weighted residuals (|CWRES| and CWRES) vs. individual predictions and time after the end of the dose. Nega-tive times denote observations taken when drug was infused, whereas positive times are observations after stopping the infusion. A dashed line denotes the line of unity or the zero line, whilst a red solid line shows a non-parametric smoother 1 10 100 11 0 100 Observed CPlasma (mg/L ) Population predictions (mg/L) 1 10 100 1 10 100 Observed CPlasma (mg/L ) Individual predictions (mg/L) 012345 |CWRES| 01 2 3 4 5 |CWRES| −4 −2 02 4 1 10 100 Individual predictions (mg/L) CWRE S −10 0 10 20 30 40 50 −4 −2 02 4
Time after end−of−dose (hr)
CWRE
S
the size-standardised volume of the distribution is constant
throughout life at 0.61 L.kg−1 for V
1 and 0.59 L kg−1 for V2.
Our estimate for PMA50 of 46.4 weeks is in good
agree-ment with earlier work by Rhodin et al. [41] who found that
glomerular filtration function reaches 50% of adult values by 47.7 weeks PMA. This suggests, in line with previous
reports [42], that vancomycin elimination depends
pre-dominantly on glomerular filtration. Moreover, our PMA50
estimate is not significantly different from the findings of
Anderson et al. [20] who reported a PMA50 of 33.3 weeks
(95% confidence interval 14.8–51.8) in a cohort of preterm neonates. It also inspires confidence that our conclusion of maturation being nearly complete at 2 years PMA is sup-ported by a recent physiologically based PK simulation
study by Calvier et al. [43].
Model building started out with an a priori model con-sisting of allometric scaling and a maturation function as
advocated by Holford et al. [11] and more recently by
Ger-movsek et al. [12]. By extending this standardised model
with an additional sigmoidal decline function, we were able to describe the deterioration in vancomycin clearance
with age. Recently, Lonsdale et al. [35] have used the same
methodology to describe beta-lactam antimicrobial pharma-cokinetics from early life to old age. Notwithstanding that tubular secretion and/or re-absorption are likely involved in
beta-lactam elimination, these authors found a PMA50
esti-mate of 49.7 weeks, which is in line with our findings. Their
estimated AGE50 of 86.8 years, however, is significantly
higher than what we found for vancomycin (61.6 years). In addition to differences in elimination processes, the differ-ent handling of renal function in the study by Lonsdale et al.
[35] compared with our analysis might explain the
differ-ent AGE50 estimates. Indeed, as seen from Table 2,
dur-ing model builddur-ing, AGE50 ranged from 67.4 to 79.8 years
depending on the method used to standardise SCR.
This is by far the largest population-PK modelling study on vancomycin pharmacokinetics. On the one hand, our findings confirm earlier fragmented findings on the influence of weight, kidney function and age on vancomycin
pharma-cokinetics by other groups [3] as well as the increased
clear-ance in patients with haematological diseases [29]. On the
other hand, we were able to negate some prior hypotheses. Fig. 3 Simulated area under
the concentration–time curve at steady state for a 24-h period (AUC 24h) according to the different patient groups in the summary of product character-istics (SmPC) and the US Food and Drug Administration (FDA) label. White boxplots show the AUC 24h distributions resulting from the original SmPC and FDA label whereas grey box-plots show the distribution of AUC 24h for the optimised doses for the SmPC and the label. The grey shaded area denotes the target exposure, i.e. an AUC 24h between 400 mg L−1 h and 700 mg L−1 h. EMA European Medicines Agency ● ● ● ●● ● ● ● ● ● ● ● ●● ●●● ● ● ●●● ● ●● ●● ●● ● ● ● ● ●●● ● ●●● ●● ●● ●●● ●● ● ● ●●●●● ●●●●● ● ● ● ● ● ●● ●● ●● ● ● ● ● ● ● ● ● ● ●● ● ●● ● ●● ●●●●●● ● ● ●● ● ●● ● ● ●●●● ● ● ● ● ●●● ● ●● ● ●● ● ● ●●● ● ●● ● ● ● ● ●●●●●● ●● ● ●● ●● ●● ● ● ● ● ● ● ● ● ● ● ● ●●
SmPC (EMA) Label (FDA)
100 200 400 7001000 2000 100 200 400 7001000 2000
newborns children & adolescents adults elderly very elderly underweight obese AUC24h(mg L−1h)
We found that after correcting for age, body size and kidney function, PK parameters were not different between patients
with or without burns [23], between critically ill or
non-critically ill patients [25], or between patients treated with
intermittent or continuous dosing [44]. In addition, we found
no differences in PK parameters with respect to the different vancomycin assay methods used (i.e. assays based on fluo-rescence polarisation or turbidimetric inhibition principles)
[45]. Supportive evidence for these findings is provided in
Figs. S6–S9 of the ESM.
Patients from two studies differed significantly from the rest of the population, thereby forcing us to include two study-specific parameters. First, patients in the Buelga et al.
study [29] had a significantly higher clearance. This finding
is in line with earlier work by Jarkowski et al. [46] and Zhao
et al. [47] who found higher clearance in adult and paediatric
patients with malignant haematological diseases. Second, the concentration–time profile for patients in the Lo et al.
study [32] was different from other studies. This is likely
owing to the heel prick sampling that was used in the Lo et al. study as opposed to venous or arterial blood sampling
in the other studies. This reasoning is in line with earlier work by Chiou who showed that drug concentrations depend
on the sampling site [48].
Using the post hoc PK parameters derived from our model, we evaluated two currently used dosing regimens for vancomycin and showed that these dosing regimens do not consistently result in efficacious and safe steady-state vancomycin exposure across patient populations. The opti-mised daily doses increase the proportion of patients
attain-ing an AUC 24h between 400 and 700 mg L−1 h for both the
European Medicines Agency-approved SmPC and the FDA-approved label. From these simulations, we see that weight-based dosing for neonates is acceptable, yet the dose-per-kil-ogram should be increased. For adults, weight-based dosing is inappropriate and results in under-dosing of underweight adult patients whilst obese adult patients are generally over-dosed. Moreover, age- or kidney function-adjusted dosing is necessary to avoid over-dosing in elderly patients and very elderly patients. The optimised FDA label, which defines kidney function-adjusted doses for patients aged older than 18 years and weight-based dosing otherwise, performs well Table 4 Posology from the US Food and Drug Administration (FDA)
label for “Vancomycin Hydrochloride for Injection USP” from the FDA website (www.fda.gov; consulted on 23 May, 2018) and the
summary of product characteristics for “Vancomycin 500 mg Powder for Solution for Infusion” available from www.medic ines.org.uk (con-sulted on 23 May, 2018)
ND not determined, as our study only included two adult patients with eGFR < 10 mL min−1, PMA postmenstrual age, PNA postnatal age a eGFR
adult estimated glomerular filtration rate according to: eGFRadults
(
mLmin−1)= Weight(kg)×(140−age(yr))
72×serum creatinine(mgdL−1)× 0.85 (if female) or
eGFRadults
(
mLmin−1)=Weight(kg)×(140−age(yr))
serum creatinine(μmolL−1)× 1.04(if female) × 1.23(if male)
b eGFR
peds: estimated glomerular fitration rate according to: eGFRpeds ( mLmin−11.73 m−2)= Height(cm)×0.413 serum creatinine(mgdL−1) or eGFRpeds ( mLmin−11.73 m−2)= Height(cm)×36.2 serum creatinine(μmolL−1)
FDA label for “Vancomycin Hydrochloride for Injection USP” Summary of product characteristics for “Vancomycin 500 mg Powder for Solution for Infusion”
Patient subgroup Renal function
adjustments Daily dose Optimised daily dose Patient subgroup Renal function adjustments Daily dose (mg kg−1) Optimised daily dose (mg kg−1) Neonates < 1 wk PNA – 20 mg kg −1 25.0 mg kg−1 Neonates < 29 wk PMA 15 23.5 Neonates < 1 mo PNA – 30 mg kg −1 34.0 mg kg−1 Neonates < 35 wk PMA 30 35.0 1 mo PNA > chil-dren > 18 yr – 40 mg kg −1 61.0 mg kg−1 Neonates < 1 mo PNA 45 54.0
Adults – 2000 mg 3000 mg 1 mo PNA >
chil-dren > 12 y eGFRpeds
b ≤ 29 15 19.0
Adults with impaired renal function
eGFRadulta < 100 1545 mg 1800 mg eGFRpeds ≤ 50 30 28.5
eGFRadult < 90 1390 mg 1800 mg eGFRpeds > 50 40 73.0
eGFRadult < 80 1235 mg 1650 mg Adults eGFRadult < 50 15 14.5
eGFRadult < 70 1080 mg 1550 mg eGFRadult ≥ 50 40 43.0
eGFRadult < 60 925 mg 1450 mg eGFRadult < 50 770 mg 1200 mg eGFRadult < 40 620 mg 900 mg eGFRadult < 30 465 mg 650 mg eGFRadult < 20 310 mg 350 mg eGFRadult < 10 155 mg ND
with consistent target attainment and minimal (± 20%) risk of under- and over-dosing across patient subgroups.
These recommendations should be interpreted by taking into account that: (1) further optimisation of these dosing regimens could be achieved by further stratifying patient subgroups based on age and/or weight; (2) the thresholds
used for defining adequate and or excessive AUC 24h are still
under debate and regional differences exist in minimum inhibitory concentration distributions; and (3) TDM is still necessary to further optimise the treatment of individual patients. Furthermore, our study excluded specific patient categories (patients receiving renal replacement therapy, haemodialysis, haemodiafiltration and extra-corporeal mem-brane oxygenation) and in the pooled dataset some patient categories were only sparsely populated (e.g. the group of children and adolescents). As such, the generalisability of our results and the predictive performance of the final model should be validated in a prospective study prior to implementation of the model or derived recommendations in clinical practice.
5 Conclusion
In this article, we show that vancomycin pharmacokinet-ics changes dramatically throughout human life and a sin-gle population-PK model is able to capture these changes. Through simulations, we showed that current dosing regi-mens do not succeed in providing similar steady-state expo-sure across patient subgroups and as such the probability for therapeutic success or vancomycin-induced toxicity is not constant throughout life. As illustrated in this work, this new model has the potential to overcome these limitations and could be used to further develop age- and renal func-tion-specific dosing regimens for vancomycin. Furthermore, this model could facilitate individualised vancomycin dos-ing through Bayesian forecastdos-ing based on therapeutic drug monitoring.
Author Contributions Peter J. Colin: idea generation, data analysis and first draft of the paper; Karel Allegaert, Alison H. Thomson, Daan J. Touw, Michael Dolton, Matthijs de Hoog, Jason A. Roberts, Eyob D. Adane, Masato Yamamoto, Dolores Santos-Buelga, Ana Martín-Suarez, Nicolas Simon, Fabio S. Taccone, Yoke-Lin Lo, Emilia Barcia: data for analysis, revision of draft manuscript; Michel M. R. F. Struys, Douglas J. Eleveld: data analysis and revision of the draft manuscript. Compliance with Ethical Standards
Funding No funding was received for this study. All costs were covered by departmental funding.
Conflict of interest Pieter J. Colin, Karel Allegaert, Alison H.
Thom-son, Michael Dolton, Eyob D. Adane, Masato Yamamoto, Dolores
Santos-Buelga, Ana Martín-Suarez, Nicolas Simon, Fabio S. Tac-cone, Yoke-Lin Lo, Emilia Barcia and Douglas J. Eleveld have no conflicts of interest that are directly relevant to the contents of this article. Daan J. Touw reports funding outside the submitted work from: ZONMW, Chiesi and Astellas. Douglas J. Touw is a member of Sanquin Blood Bank Medical Advisory Board, an honorary member of the editorial board of Clinical Pharmacokinetics and a member of the editorial board of the Journal of Cystic Fibrosis. Jason A. Roberts has received funding from the Australian National Health and Medical Research Council for a Centre of Research Excellence (APP1099452) and a Practitioner Fellowship (APP1048652); has consultancies with Astellas, Biomerieux, Accelerate Diagnostics and Bayer as well as investigator-initiated studies with MSD, Cardeas and The Medicines Company, all outside the submitted work. Michel M. R. F. Struys re-search group/department received grants and funding from The Medi-cines Company (Parsippany, NJ, USA), Masimo (Irvine, CA, USA), Fresenius (Bad Homburg, Germany), Acacia Design (Maastricht, the Netherlands) and Medtronic (Dublin, Ireland) and received honoraria from The Medicines Company, Masimo, Fresenius, Baxter (Deerfield, IL, USA), Medtronic and Demed Medical (Temse, Belgium). He is an editorial board member of the British Journal of Anaesthesia and a senior editor of Anesthesia & Analgesia.
Open Access This article is distributed under the terms of the
Crea-tive Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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Affiliations
Pieter J. Colin1,2 · Karel Allegaert3,4,5 · Alison H. Thomson6 · Daan J. Touw7,8 · Michael Dolton9 · Matthijs de Hoog10 ·
Jason A. Roberts11 · Eyob D. Adane12 · Masato Yamamoto13 · Dolores Santos‑Buelga14 · Ana Martín‑Suarez14 ·
Nicolas Simon15 · Fabio S. Taccone16 · Yoke‑Lin Lo17,18 · Emilia Barcia19 · Michel M. R. F. Struys1,20 · Douglas J. Eleveld1
1 Department of Anesthesiology, University Medical Center Groningen, University of Groningen, P.O. Box 30001, 9700 RB Groningen, The Netherlands
2 Laboratory of Medical Biochemistry and Clinical Analysis, Faculty of Pharmaceutical Sciences, Ghent University, Ghent, Belgium
3 Pediatric Intensive Care, Erasmus MC, Sophia Children’s Hospital, Rotterdam, The Netherlands
4 Department of Neonatology, Erasmus MC, Sophia Children’s Hospital, Rotterdam, The Netherlands
5 Department of Development and Regeneration, KU Leuven, Louvain, Belgium
6 Strathclyde Institute of Pharmacy and Biomedical Sciences, University of Strathclyde, Glasgow, UK
7 Department of Clinical Pharmacy and Pharmacology, University Medical Center Groningen, University of Groningen, Groningen, The Netherlands
8 Department of Pharmacy, Section Pharmacokinetics, Toxicology and Targeting, University of Groningen, Groningen, The Netherlands
9 Faculty of Pharmacy, University of Sydney, Sydney, NSW, Australia
10 Department of Pediatrics, Erasmus University and University Hospital Rotterdam/Sophia Children’s Hospital, Rotterdam, The Netherlands
11 University of Queensland Centre for Clinical Research and School of Pharmacy, The University of Queensland, Brisbane, QLD, Australia
12 Raabe College of Pharmacy, Ohio Northern University, Ada, OH, USA
13 Department of Neuropsychopharmacology and Hospital Pharmacy, Nagoya University Graduate School of Medicine, Nagoya, Japan
14 Department of Pharmacy and Pharmaceutical Technology, University of Salamanca, Salamanca, Spain
15 Aix-Marseille University, INSERM, IRD, SESSTIM, Hop Sainte Marguerite, Service de Pharmacologie Clinique, CAP, Marseille, France
16 Department of Intensive Care, Erasme Hospital, Université Libre de Bruxelles, Brussels, Belgium
17 Department of Pharmacy, Faculty of Medicine, University of Malaya, Kuala Lumpur, Malaysia
18 Department of Pharmacy Practice, School of Pharmacy, International Medical University, Kuala Lumpur, Malaysia 19 Department of Pharmaceutics and Food Technology, School
of Pharmacy, Universidad Complutense de Madrid, Madrid, Spain
20 Department of Anesthesia and Peri-operative Medicine, Ghent University, Ghent, Belgium
